So, I live in Tel Aviv and do mot of my surfing here. Up and down the coast in the city there are several good spots but the most popular are Hilton beach, the Dolphinarium and Hof Maravi (near Jaffa).
If you've never surfed in Israel you're looking at lots of days of waiting for any waves at all and avg surf days are waist to chest high. The good news is the scene is pretty chilled out here and most of the year you can surf in trunks.

What kind of breaks are there? All sand bottom? or any reefs? Are there any surf shops out there? I bet there are some good places to eat after surfing too.

Most of the breaks are sand breaks and they usually break in fairly shallow spots unless its a big day.
Every surfable spot in Tel Aviv and vicinity is walking distance to at least one beach restaurant. The beach life is pretty awesome because the weather is so warm so there are cafes up and down the beaches that stay open from breakfast late into the night.